Answer:
x > -6
Step-by-step explanation:
Here in this question, we have to solve for x from the given inequality
-6 > -30- 4x.
We can solve the inequality equation by using the properties of inequality.
We have, -6 > -30 -4x
⇒ -6+30 > -4x
{The summation and subtraction rules of the inequality equation is similar to that of ordinary equations}
⇒24 > -4x
Dividing both sides by -1, we get,
⇒-24 < 4x
{In case of division of both the sides of an inequality by a negative number, the inequality sign changes from > to < and vice-versa}
⇒4x > -24
Dividing both the sides by 4, we get
⇒ x > -6 {There is same rule as equality equation for division both sides by a positive number} (Answer)
Answer: Option A is correct.
Step-by-step explanation:
- The correlation coefficient(r) is a statistical measure that computes the strength of the relationship between two variables.
It lies between -1 and 1.
If the correlation coefficient in an ordinary least squares regression = 1.00.
That indicates that there is a perfect relationship between the variables.
i.e. all the data points must fall exactly on a straight line with a positive slope. .
[when r is positive, the slope of the line is positive].
i.e. option A is correct.
Answer:
83 is the largest number
Step-by-step explanation:
x, x+2, x+4
x + (x + 2) + (x + 4) = 243
3x + 6 = 243
3x = 237
x = 79
<span>The two points that are most distant from (-1,0) are
exactly (1/3, 4sqrt(2)/3) and (1/3, -4sqrt(2)/3)
approximately (0.3333333, 1.885618) and (0.3333333, -1.885618)
Rewriting to express Y as a function of X, we get
4x^2 + y^2 = 4
y^2 = 4 - 4x^2
y = +/- sqrt(4 - 4x^2)
So that indicates that the range of values for X is -1 to 1.
Also the range of values for Y is from -2 to 2.
Additionally, the ellipse is centered upon the origin and is symmetrical to both the X and Y axis.
So let's just look at the positive Y values and upon finding the maximum distance, simply reflect that point across the X axis. So
y = sqrt(4-4x^2)
distance is
sqrt((x + 1)^2 + sqrt(4-4x^2)^2)
=sqrt(x^2 + 2x + 1 + 4 - 4x^2)
=sqrt(-3x^2 + 2x + 5)
And to simplify things, the maximum distance will also have the maximum squared distance, so square the equation, giving
-3x^2 + 2x + 5
Now the maximum will happen where the first derivative is equal to 0, so calculate the first derivative.
d = -3x^2 + 2x + 5
d' = -6x + 2
And set d' to 0 and solve for x, so
0 = -6x + 2
-2 = -6x
1/3 = x
So the furthest point will be where X = 1/3. Calculate those points using (1) above.
y = +/- sqrt(4 - 4x^2)
y = +/- sqrt(4 - 4(1/3)^2)
y = +/- sqrt(4 - 4(1/9))
y = +/- sqrt(4 - 4/9)
y = +/- sqrt(3 5/9)
y = +/- sqrt(32)/sqrt(9)
y = +/- 4sqrt(2)/3
y is approximately +/- 1.885618</span>
Answer:
-ab/1
Step-by-step explanation:
The multiplicative inverse of x/y is y/x, because when multiplied it equals 1.
x/y time y/x = xy/xy, which equals one.
In this case, -1/ab times -ab/1 = -1ab/-1ab, which equals one.